Abstract

The design of an off-axis mirror system, based on a pair of prolate spheroids with a common focus but not a common axis, is considered. With the focus as a pupil, any ray through one focus of a spheroid must pass through all others as each such ray becomes a chief ray. A pseudo- (optical) axis is defined as that chief ray about which other rays are symmetric. A condition to ensure the existence of the pseudoaxis is derived based on a relation between the two eccentricities, the angle that the pseudoaxis makes with the axis of the first spheroid and the angle between the axes of the two spheroids. Data are presented to compare theoretical calculations with computerized real ray-tracing data. A brief discussion is presented to consider the problem of imaging formation.

References

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a The pseudoaxis is a function of the eccentricities and the angle subtended by the axes of the two spheroids as derived in Eqs. (29) and (38). Radii are not considered. These values and intermediate values of Eqs. (20), (22), (26), and (34) are indicated.

a The angular directions of several rays are calculated from the proximal focus of the first spheroid defined in Table 1 with respect to the pseudoaxis at an angle θ. The units are all in degrees. Note that the rays are symmetric with respect to the pseudoaxis, as indicated by the angle ψ‴.

a Rays are again calculated through the proximal focus of the same first spheroid of Table 1 with respect to the pseudoaxis at an angle θ. These data are generated by using standard ray-tracing software, assuming matching vertex radii of curvature, r = 100 mm. Note that the rays are again symmetric with respect to the pseudoaxis, as indicated by the angle ψ‴.

a The pseudoaxis is a function of the eccentricities and the angle subtended by the axes of the two spheroids as derived in Eqs. (29) and (38). Radii are not considered. These values and intermediate values of Eqs. (20), (22), (26), and (34) are indicated.

a The angular directions of several rays are calculated from the proximal focus of the first spheroid defined in Table 1 with respect to the pseudoaxis at an angle θ. The units are all in degrees. Note that the rays are symmetric with respect to the pseudoaxis, as indicated by the angle ψ‴.

a Rays are again calculated through the proximal focus of the same first spheroid of Table 1 with respect to the pseudoaxis at an angle θ. These data are generated by using standard ray-tracing software, assuming matching vertex radii of curvature, r = 100 mm. Note that the rays are again symmetric with respect to the pseudoaxis, as indicated by the angle ψ‴.